Answer to Question #155608 in Quantum Mechanics for ayesha

Question

Find the ground-state electron energy by substituting the radial wave function, 𝑅(𝑟)= 2𝑎𝑜3/2𝑒−𝑟𝑎𝑜⁄ that corresponds to 𝑛 = 1,𝑙 = 0, into radial equation for hydrogen atom.

Answer 1

Solution

Given radial wavefunction

$R(r)= (\frac {1}{2a_0})^{\frac {3}{2}} e^{-r/a_0}$

For H- atom enegy is given

$E_n = - \dfrac {m_ee^4}{8 \epsilon ^2_0 h^2 n^2}$

For ground state energy n=1, l=0, m=0

Putting all value then

Ground state energy become

$E_0=-13.6eV$